Gradients through spin wave calculations

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Suppose we have a "loss function" $\chi^2$ as a function of intensity data. It will typically be straightforward to calculate the gradient of $\chi^2$ with respect to the intensity. Then, using the chain rule, we would like to contract this with the gradient of the intensity with respect to the Hamiltonian parameters. For this, we need to apply a perturbation theory associated with the para-unitary Bogoliubov transformation. It will also require a machinery for Sunny to keep track of the free parameters in a Hamiltonian.